Question: Simplify; express your answer in exponential form. Assume $t\neq 0, q\neq 0$. $\dfrac{{t^{4}}}{{(t^{-5}q^{3})^{-1}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${t^{4} = t^{4}}$ In the denominator, we can use the distributive property of exponents. ${(t^{-5}q^{3})^{-1} = (t^{-5})^{-1}(q^{3})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{t^{4}}}{{(t^{-5}q^{3})^{-1}}} = \dfrac{{t^{4}}}{{t^{5}q^{-3}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{4}}}{{t^{5}q^{-3}}} = \dfrac{{t^{4}}}{{t^{5}}} \cdot \dfrac{{1}}{{q^{-3}}} = t^{{4} - {5}} \cdot q^{- {(-3)}} = t^{-1}q^{3}$.